Impossible to vary square wave FREQUENCY output based on a PWM input?

I'd start in a place like this one: https://www.arduino.cc/en/Tutorial/SecretsOfArduinoPWM
Coincidentally (or not?) it's also the place where your 'everyone' got their poor suggestion from - moreover, it outlines why it's not an optimal solution to do this with digitalWrites & delayMicroseconds. Read on after that bit as it gets interesting.

Well, perhaps if it's done poorly, but in principle the approach could/should work. What kind of noise did you experience, and what kind of approach did you try exactly? Perhaps if you post a schematic of your attempt someone can comment on it.